The present invention relates to a method and a system of process control comprising in combination a feed-back control and a feed-forward control, particularly useful in implementing a direct digital control.
In a process control system, a feed-back control system plays an important role, but the feed-back system operates responsive to the change in the controlled variable and executes a required correction only after the controlled variable deviates from a set value or target value. Therefore, there arises no problem as far as the controlled variable varies slowly, but the feed-back control system has the serious defect that its transient response is delayed when a sudden variation in disturbance occurs because the feed-back correction is made only after the controlled variable deviates from a target value. A solution to this problem is to use, in combination with the feed-back control system, a feed-forward control system in which disturbances are detected and a correction or compensation based on prediction is made before the controlled variable is actually affected.
FIG. 1 shows a fundamental control system comprising in combination a feed-back system and a feed-forward system. A comparator 1 compares a controlled variable with a target value and the result of this comparison; i.e., difference between the target value and the controlled variable is fed to a PID controller 2. The output of the PID controller 2 is fed to an adder or sum node 3. Meanwhile a disturbance D, which is transmitted through an imaginary path 7 with a transfer function G.sub.D, affects the controlled variable X. In order to compensate for or counteract the adverse effects of disturbance D on the controlled variable X, the disturbance D is transmitted through a feed-forward model 8 with a transfer function G.sub.F to the adder 3 to be added to the output from the controller 2. The resulting output from the adder 3 is fed as a manipulated variable to a controlled process 10, and the effect of the manipulated variable transmits through an imaginary path 4 with a transfer function G.sub.P. The effect of the disturbance through the path 7 and the effect of the manipulated variable M are effectively added to become the controlled variable X. For illustration, this summation is shown to be effected by an adder or sum node 5.
Therefore, if the output from the controller 2 is designated by Y, the controlled variable X is given by ##EQU1## From equation (1) it is readily seen that, in order that the controlled variable X may be free from any adverse effects from the disturbance, the following condition must be satisfied: EQU G.sub.D +G.sub.F. G.sub.P =0
It follows that the transfer function G.sub.F of the feed-forward model 8 must be EQU G.sub.F =-G.sub.D /G.sub.P (2)
In general, the transfer functions G.sub.D and G.sub.P may be approximated in terms of a combination of a first-order time-lag and a dead time as follows: ##EQU2## where K.sub.P and K.sub.D are gain constants, respectively;
T.sub.P and T.sub.D are time constants, respectively; and PA0 L.sub.P and L.sub.D are dead times, respectively. PA0 Hs is the latent heat of the steam; PA0 Fi is the flow rate of the raw material; PA0 Ci is the specific heat of the raw material; PA0 Ts is the set or target value for the temperature at the outlet of the heat-exchanger; PA0 Ti is the temperature at the inlet of the heat-exchanger; and PA0 .eta. is the efficiency of the heat-exchanger. PA0 T.sub.P is the time constant from the time when the steam flow rate is set (that is, when the output is derived from the adder 20) to the time when the temperature at the outlet of the heat-exchanger 14 is affected by this flow rate set. PA0 (1) the variations in temperature of raw material; PA0 (2) the variations in efficiency of the heat-exchanger; PA0 (3) the variations in the latent heat of the steam; PA0 (4) the variations in ambient temperature; and PA0 (5) the variations of the specific heat of raw material.
It follows that the transfer function G.sub.F of the feed-forward model 8 is given by ##EQU3## If the dead time of G.sub.P and dead time of G.sub.D are substantially the same, Eq. (3) may be rewritten in the form of ##EQU4## The thus simplified equation (4) is often used in practical applications. However, it sometimes occurs that the characteristic of the particular process on which the feed-forward control is effected is not correctly approximated by the first order equation (4), or the characteristic of the process is not linear. In addition, the process control system has various limitations and is subjected to various conditions. As a result, the prior art feed-forward system has encountered the following problems:
(1) It is not possible to set or adjust, independently of each other, gains of the static and dynamic compensation components of the disturbance compensation, while such independent setting is desirable to adapt the system to the process characteristics. It is noted, in this connection, that setting of the gain can involve setting different gains for different directions of changes (increase and decrease) i.e., different polarities or signs of the compensation value;
(2) It is not possible to provide a dead band or zone only for the static compensation component alone or dynamic compensation component alone. The provision of dead zone nullifies the feed-forward control while the change of the disturbance is small.
It is not possible to set the dead zones of the two components independently of each other;
(3) It is not possible to provide upper and lower limits to the static compensation component alone or to the dynamic compensation component alone. It is not possible to set the limit values of the two components independently of each other;
(4) It is difficult to achieve a "bumpless" switching when the controller 2 is switched between the automatic and manual controls (especially where a velocity type controller is in use); and
(5) It is difficult to analyze and understand the qualitative significance of the feed-forward control, so that the adjustment of the controller is difficult.
Moreover, where a velocity type PID controller is used, the prior art feed-forward system has the following drawbacks.
As shown in FIG. 2, where the PID controller 2 is of a velocity type, the output of the feed-forward model 8 is converted by a position type to velocity type converter or a difference detector 9 before being applied to the adder 3. The output of the adder 3 is then converted by a velocity type to position type converter 6 and is thereafter used as the manipulated variable M of the process.
Upon relatively large stepping change in the disturbance, the manipulated variable M will change as shown in FIG. 3A whereas what is desirable is as shown in FIG. 3B. This is because the converter 6 does not follow increase further than its maximum (100%) while its output begins to drop immediately when the input becomes negative, and hence the amount DR of the total drop from the 100% level in FIG. 3A equals the amount DR of the total drop from the desirable peak in FIG. 3B. Such characteristics are given to the converter 6 for the purpose of cancelling or counteracting reset windup effects of the controller 2. Thus, the actual response (FIG. 3A) differing from the desirable response (FIG. 3B) gives adverse effects on the process control.
A similar situation, but with opposite polarity, will occur when the direction of the change is opposite and the desirable output of the converter 6 exceeds the lower limit of 0%.
Furthermore, the prior art feed-forward system has the following shortcomings. That is, in the above-described analysis of the feed-forward control system, it has been assumed that the gain coefficient K.sub.D of the transfer function G.sub.D of the disturbance D be constant and consequently that the gain coefficient K.sub.F =K.sub.D /K.sub.P of the feed-forward model 8 be constant. Actually, however, the disturbance coefficient K.sub.D is not fixed, and varies irregularly and widely depending upon such factors as indirect disturbances, variations in characteristics with the passage of time, variations in physical quantities inside and outside of the process control system, variations of chemical compositions, variations in ambient temperature, disturbances which are not detected or cannot be detected and so on. As a result, the feed-forward control system cannot attain desired effects and may adversely affect the process control.
Meanwhile, because of diversity of raw materials, fuels and products, variations in load due to variations in the rate of operation made in view of changes in economical conditions, increasing demand for multipurpose system and the like, there has been an increasing demand for flexibility of the process and hence the control system. This situation is explained in further detail taking, as an example, control on the temperature at the outlet of a heat-exchanger system with reference to FIG. 4.
In FIG. 4, a raw material 11 is fed through a feed line 12 to a heat-exchanger 14, heated by the steam, and is discharged therefrom. A temperature sensor 15 detects the outlet temperature T.sub.0 of the heat-exchanger 14 and generates a signal representative of the detected outlet temperature T.sub.0. This signal is applied to a temperature controller 19, which controls the heat-exchanger system to maintain the outlet temperature T.sub.0 at a predetermined level.
A flow-rate sensor 13 detects the flow rate Fi of the raw material 11 and generates a signal representative of the detected flow rate Fi. This signal is applied to a feed-forward model 21. The output from the feed-forward model 21 and the output from the temperature controller 19 are added in an adder 20, which applies the sum signal, as a target value, to a steam flow-rate controller 22. The steam flow-rate controller 22 receives the output of the steam flow-rate sensor 17 as a feed-back signal and executes control operations for maintaining the feed-back signal at the target value. The output from the steam flow-rate controller 22 is used to control a control valve 18. In this way, the outlet temperature T.sub.0 of the heat exchanger 14 is maintained constant.
The transfer function G.sub.F of the feed-forward model 21 will now be discussed. First, the heat balance Q in the steady state of the process is obtained by the following equation: ##EQU5## where Fs is the flow rate in weight of steam;
Eq. (5) is rewritten so as to obtain the steam flow rate Fs which is the controlled variable. Then, ##EQU6## From Eq. (6), the static compensation component G.sub.FS of the feed-forward model 21 is obtained as follows: ##EQU7## The transfer function G.sub.F with the dynamic compensation component of the feed-forward model 21 is ##EQU8## where T.sub.D is the time constant from the raw material flow rate sensor 13 to the outlet temperature sensor 15; and
So far, only the variation in raw material flow rate Fi is considered as disturbance affecting the feed-forward control system and it has been assumed that ##EQU9## be constant, but actually K.sub.F varies irregularly over a wide range depending upon the following factors:
As a result, the feed-forward system cannot attain the satisfactory results. More particularly, the controllability is adversely affected when raw material flow rate varies. This results in fluctuation of the product's quality.
As described above, in the prior art combined feed-back and feed-forward control system, satisfactory effects cannot be attained and adverse effects are sometimes brought about. This problem is thus becoming more and more serious as the demand for the flexibility of the process grows.